Oily coffee beans

So we have a Gaggia Brera superautomatic espresso maker. It makes great espresso but refuses to feed oily coffee beans. Here's a list of those that aren't and those that are too oily.

Not too oily:

• Nicoletti Coffee Espresso Roast Beans https://www.nicoletticoffee.com/
• Most of the actual Italian beans, such as those from Lavazza

In between

• Verena Street Shot Tower Espresso

Too oily:

• Dazbog White Nights Espresso
• Kicking Horse Cliff Hanger Espresso
• Kicking Horse Three Sisters

It'd be nice if the roasters would come up with a method to express this. In general of course, we can look for light or medium roast, but there is little consistency between the light/medium/dark roast oiliness.